Ray Anderson's Pocket Brass Band is about watch-pocket size: With three horns and drums, it couldn't get much smaller. On its new Sweet Chicago Suite, Anderson makes what the group does sound easy. Just write some catchy, bluesy tunes and then have the band blast them out.

Brass bands are usually at least twice as big as this quartet. It's tricky making a little band sound this big, Ray Anderson knows his tricks. The loose harmonizing and rough tone suggest a blurry high-school half-time outfit; so do Anderson's multi-part tunes, which are ready-made for marching. The old Sousa concert bands featured showy brass players. Trombonist Anderson and trumpeter Lew Soloff improvise together, shadow each other and fill in the other guy's backgrounds. Nobody just stands around.

The rhythm section makes a racket, too. New Orleans' Matt Perrine plays sousaphone, the marcher's tuba. His presence is one reason Anderson's suite for his hometown Chicago — the wooden back stairs, the rowdy community meetings, the old Maxwell Street market — can sound like St. Charles Avenue on Mardi Gras. But then Chicago was the first place early New Orleans jazz players settled up north, bringing their vocalized brass techniques. And both cities love a blues mambo.

An outsize drummer will really make a compact band sound bigger, and this quartet has one in Bobby Previte. The pianist Stephanie Stone, who saw the great swing-era drummers up close, always says Previte has that same kind of big-beat charisma. There aren't so many moderns who echo Gene Krupa at the tom-toms.

Ray Anderson's Pocket Brass Band was deep into a tour when it recorded Sweet Chicago Suite in 2010 — that's partly why the group sounds so tight and revved up. But it had been playing together for 12 years by then, and Anderson wrote most of this music in 2001. It's a sign of the dismal state of the record business that it's only coming out now, but good things come to those who wait.